The function f(x) = 2.9√x + 20.1 models the median height, f(x), in inches, of boys who are x months of age. The graph of f is shown.
Solve, a. Describe how the graph can be obtained using transformations of the square root function f(x) = √x.
b. According to the model, what is the median height of boys who are 48 months, or four years, old? Use a calculator and round to the nearest tenth of an inch. The actual median height for boys at 48 months is 40.8 inches. How well does the model describe the actual height?
c. Use the model to find the average rate of change, in inches per month, between birth and 10 months. Round to the nearest tenth.
d. Use the model to find the average rate of change, in inches per month, between 50 and 60 months. Round to the nearest tenth. How does this compare with your answer in part (c)? How is this difference shown by the graph?
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